[saspinski (OP)]

When deriving the Schwartchild solution, the Einstein tensor is equal to zero. By spherical simmetry considerations, after calculating all Christoffel symbols, we get the metric, where the g₀₀ and g₁₁ have a constant divided by r. If we require that the Newton gravity law must be valid for low velocities, that constant is GM. And it is interpreted as a point mass in the center, or a spherical simmetrical distribution of mass. In the later case, the metric is valid only outside the body.

I wonder if we allowed regions of spacetime have Schwartchild metrics without requiring Newton law for low speeds. And keep an arbitrary constant there, not putting a mass to explain the field.

After billions of years, dust from the surroudings would not "fill the voids" with mass?

And couldn't an intelligent man, after inventing calculus, looking at that bodies, conclude that mass is the cause of an attraction force that explain the planets orbits? When it was really a consequence of the metric?
 
We could raise an objection about why a metric like that, instead of a Minkowski one. But it is like asking why everything is moving, instead of at rest, or why Being, instead of Nothing.

The reason of that idea is the fact that for vacuum solutions the energy-moment tensor is zero, and mass is not required to calculate the metric.

[chris]

Any takers?

[jeffreyH]

You may be talking about rest mass here, rather than mass in general. It is not simply mass that would generate a gravitational field. Due to equivalence energy causes gravitational fields. This means that you would have to take into account boson fields when determining the metric. The problem here is that the electromagnetic field will dominate.

P.S. Do bosons such as the photon depend upon massive particles to exist or can they exist independently? The field arises via massive particles so it is a bit like the chicken and egg.

[sceptic-eng]

I agree that the electomagnetic forces dominate.  In fact the WMAP result indicates that dark energy is expanding the universe with a repelling force of 24 times the force of the  gravity that is attracting it together. Thus to balance their findings we need the reciprocal of the 95% missing dark universe and that missing dark force could be an electrostatic star repelling force 

[sceptic-eng]

To balance the universe electrostatically needs a dark energy repelling force 24 times stronger than gravity force. But to balance the solar system we require a force that attracts planets to the sun/star of similar magnitude and further a sideways dark matter force that can spin the negative matter planets around which is probably a magnetic spin force.  Is it possible do you think?
ACSINUK

[jeffreyH]

@sceptic-eng Your own theories speculations do not belong in this section of the forum.

[sceptic-eng]

Yes, it is speculation but where is the proof that electromagnetic fields do not exist in space?  Have you a link that positively proves that fields do not exist and from which electromagnetic zero reference point in the universe are they measured from?  I still remain a sceptical engineer.